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3 years ago

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

1 answer:

3 0

F(x) = x² + 4x + 10

f(x) - 10 = x² + 4x

perfect square:
x² + 4x + 4 ⇒ (x + 2)²

(x + 2)² = x(x+2) + 2(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

f(x) - 10 + 4 = x² + 4x + 4
f(x) - 6 = (x+2)²
f(x) = (x+2)² + 6

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Given the following functions, find and simplify (f • g)(x) f(x)=—x+3 g(x)=-x-1

Hitman42 [59]

Answer:

$(f\circ g)(x)= x + 4$

Step-by-step explanation:

Composite Function

Given f(x) and g(x) as real functions, the composite function $(f\circ g)(x)$ is defined as:

$(f\circ g)(x)=f(g(x))$

It can be found by substituting g into f.

We are given the functions:

f(x) = -x + 3

g(x) = -x -1

Find

$(f\circ g)(x)=f(g(x))= - (-x -1) + 3$

Removing parentheses:

$(f\circ g)(x)= x + 1 + 3$

Simplifying:

$\mathbf{(f\circ g)(x)= x + 4}$

5 0

3 years ago

1.)A rectangle has an area of 72 square centimeters and the length is twice the width. The perimeter of the rectangle

Greeley [361]

area = L x w = 72

L = 2w

72 = 2w*w = 2w^2

divide by 2

36 = w^2

w = sqrt(36) = 6

l = 2*6 =12

perimeter = 2L +2W = 2*12 + 2*6 = 24+12 = 36

sqrt(40)= 6.324555 cm ( round to 6.32 )

6.32 - 4 = 2.32 cm original length of a side

7 0

3 years ago

Solve for x -3x+6=2x-24 -30 -6 6 30

Svetach [21]

-3x + 6 = 2x - 24.

Add 3x to both sides.

6 = 5x - 24.

Add 24 to both sides.

30 = 5x.

Divide it all by 5.

x = 6.

8 0

3 years ago

Prove that in each triangle the total angles are 180 degrees

dmitriy555 [2]

This is a proof that the angles in a triangle equal 180°:

The top line (that touches the top of the triangle) is
running parallel to the base of the triangle.

So:

angles A are the same angles B are the same

And you can easily see that A + C + B does a complete rotation from one side of the straight line to the other, or 180°

8 0

3 years ago

Read 2 more answers

Mary Sweet works in a pizza store where busiest days fall on the weekend.

aliya0001 [1]

Answer:

$10.75 x 3 1/2 = $37.625 (rounded to the nearest cent: $37.63). $10.75 x 5 = $53.75. $37.625 + $53.75 = $91.375. (rounded to the nearest cent: $91.38) hope this helps

Step-by-step explanation:

- Zombie

4 0

2 years ago